Wednesday, April 30, 2008

Infinite Probes2

From discussing this with various recipients , there seems to be a need for a simpler explanation . I thought I had explained it in the simplest fashion possible . The subject matter is inherently complex .

But , here goes .

How much must you save ?If you save too little , a random fluctuation can wipe you out .If you save too much , you lose opportunity costs . If you are in competition , this loss can be enough to lose the competition (ie you die)

Intuitively , you can realize there is an optimum level of saving .

Methods exist of calculating this optimum in very specific instances (ie portfolios of shares ,eg Kelly criteria , or tactics in war eg MiniMax ) .

The General CaseWe need to hold a Reserve in case Something goes wrong . But we do not know what thing goes wrong .

Infinite Probes tries to answer the general case . What is really , really surprising is that a answer is possible .

This approaches a constant , widely used in mathematics and physics .(e = 2.718…) .

All we need is a system that can be subdivided indefinitely (to infinity) .

First , we divide by 1Then 2Then 3Then 4

And so forth till infinity .

What is important is not that we do know what these divisions are , only that they are possible . We also do not know which one element goes wrong .

The other critical insight is that it is the relation between elements that is important . (Permutations) (The failure of an element in total isolation cannot affect the whole system by definition .)

We can count the number of relationships where there is failure of one element .It is n! , where n is number of divisions where only one failure .

Multiple failures are handled by summing :

Our Reserve(R ) is divided by n to infinity and summed .

TotReserve= R*( 1 + 1/2! + 1/ 3! + … 1/n! + …)TotReserve= R * e

To find the boundaries of our Reserve , we set TotReserve = Cost

Then

R = 1/e * CostR ~ 0.37 * Cost

What does this mean?This method measures the upper boundary of the reserve needed to survive failures in any element of the Cost-Universe . Ie , internal fluctuations .

This is the surprising bit . Any society that keeps at least 37% reserves , can only be destroyed by something outside it’s envelope . It is internally stable , no matter what .

Empires like the Ancient Egyptians , Romans , Chinese are possible , as long as there is no climactic fluctuation , new inventions , diseases ,etc . Rare events . Hence the technological stasis of old civilizations . The two are synonymous .

This is true at any scale (except quantal , by definition.) .

Individuals too . Humans can be seen as empires of noospheres .

The upper boundary does not take any double-counting into account . It is true for any system whatsoever .

A truly remarkable precise result from such general axioms .

The Lower Boundaries .This is where it gets interesting .Remember , we are just counting the number of ways in which permutations of one element can fail . We then sum them to get the effect of the failures of other elements

The easiest is the business that just starts and is not selling anything . It fails on n elements on every term . It’s floor capital must then beR=Cost/(1+e)R=0.27*Cost

This is the initial reserve to get off the ground .This is true in any ecosystem . This is why it is so difficult to start a new business , or why a new species cannot succeed . Or why waves of pandemics are scarcer .

For the epidemically minded , this 10% difference is responsible for the demise of the Black Death ( smallpox outcompeted bubonic plaque variants for the CR5 access site.Ironically , the reason why we have only a limited HIV plague is the high competition for this site , probably some flu vectors . As one would expect , the incidence of HIV then becomes inversely proportional to connectivity (ie flights) .

A cessation of airplane flights will then lead to a flare-up of diseases like these .Not exactly what anybody has in mind . )

When we find that we really need the spread of infectious vectors to stay healthy , then we know we have really screwed ourselves .

These are the two main boundaries .The literature is full of other limits the series can approach . Keep a clear head on what the physical significance is .

FatI cannot leave the subject without the thing closest to human hearts : appearance .Fat and fitness .Sadly , the present fad for leanness is just that . The period of superfluous food is coming to an end .Rich individuals can afford to be lean because the reserves are in the monetary wealth Women have to bear children individually , so they cannot store the needed reserves externally . Hence their fat storage is close to the theoretical optimum even in Western societies (33%) . In other societies the percentage is about 37-40% .

Human males have been bred (Mk III humans) for muscle and little fat (8% in a superbly fit male) . He does not have reserves to withstand even garrison duty (even little diseases will lay him low .) Note the frequent references to diseases laying whole armies low .

Note what is left out : the camp-followers . They survived The women and babyfat children . Every army seeded the invaded area with women and children .

The bred soldier has to eat a high-carb food frequently : not meat or fat , his body cannot store it . This is the definition of a wheat-eating legionary .

Ho ! Ho! Ho!The Atkinson diet .No wonder it does not make sense in evolutionary terms .Mesomorphic humans have been bred not to transform expensive proteins and fats into bodymass .

The soldier-class were kept on a carbohydrate leash , which could only be supplied by farming .

The Smell of Horses .

Horses exude pheromones that promote body-leanness in humans . This has an obvious advantage to horses . Horses are breeding jockeys .

The time-span is enough : at least 8 000 years . (400 generations)

Because pregnant women cannot ride horses , there was a selection pressure to breed horses who have a pheromone that block female dominance pheromones , especially since females have to weigh more because of fat-reserve considerations .

Outside a farming environment , horses will sculpt their riders as much as the riders are sculpting them .

Small Mongolian ponies , small Mongolians .

This is why alpha-males like horses and horse-dominated societies were able to conquer and keep matriarchies .

Note the effect of the pheromones on women riders . Androgeny .On males it becomes extreme blockage of oestrogen . It seems like a surge of male hormones , but it is just an imbalance . (If too much male hormones , the men just kill their horses )

This is why the auto-mobile had such a big sociological effect . No horses , so the men became more effeminate .